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It is now easier than ever to imagine a New Zealand without notes and coins - and not just for the convenience factor.

A cashless society could help combat crime and tax avoidance by making it much harder to trade illegally and in an untraced way.

It would avoid the problem of cash hoarding if interest rates were ever cut to 0 per cent, or even went into negatives. And a move to a digital currency could also allow us to do without banks for transactions and save a lot of money in processing and conversion fees.

So why don't we do it? Now that most people have smart phones and almost all retailers are connected to a payments network, it would seem a simple step to remove cash from the system.

After all, many of us use Eftpos and contactless Visa and Master cards to pay for things. Why not switch completely and remove the cost and danger of storing, transporting and handling cash?

Yet it's proving harder than many thought, and it's not just a New Zealand problem.

Despite all the gadgets and terminals, there is more cash in circulation than ever. The Reserve Bank reports that as of March last year, $4.96 billion of notes and coins was sitting in wallets and vaults and under mattresses. That's up 61.6 per cent from the $3.07b in circulation just 10 years earlier.

A lot of money was withdrawn from ATMs by worried savers during the Global Financial Crisis and has never been redeposited.

Almost $200 million was also distributed in Christchurch in the aftermath of the earthquakes to help Cantabrians get by when shops couldn't connect or use their regular payment systems.

But even with these special events, the amount of cash in the economy has been growing at surprisingly strong rates and faster than the economy as a whole.

A large part of the rise is due to STDs - sex, tax and drugs. The secret economy loves cash and it's no surprise IRD is having to launch regular crackdowns on cash jobs to ensure everyone is paying GST, PAYE and company tax.

But something else is going on, too. Extremely low inflation and not so much faith in banks, particularly in the Northern Hemisphere, has encouraged people to hold their savings in cash because their real value is not being eroded much.

The holy grail would be a type of bitcoin system that allows people to pay each other using the banking and credit card systems and avoid transaction and conversion fees that clip the ticket.

One idea suggested by the Bank of England last year was the creation of a digital currency by the central bank. It would use the "blockchain" technology at the centre of the bitcoin system, but that would be reliable and backed by the state.

Everyone would have a central bank account and simply transfer money between each other without having to pay fees.

Such a system would allow much cheaper transactions and let the central bank impose negative interest rates, once it had got rid of cash. It would be easier to police crime and reduce tax avoidance.

It all sounds like a radical idea, but it's one central banks and policy-makers worldwide are considering in other countries as they try to encourage spending, investment and efficiency in a world of deflation, crime and tax avoidance.